Details

sample33.0ms

Algorithm

intervals

Results

11.0ms

271×

body

valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	11	15
1	17	13
2	21	13
done	21	13

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.7b

localize10.0ms

Local error

Found 2 expressions with local error:

0.8b	(fma a c (* b d))
24.2b	(/ (fma a c (* b d)) (fma c c (* d d)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
4×	`add-exp-log` `add-cbrt-cube`
3×	`associate-/r` `associate-/l`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

2 → 39

Calls

2 calls:

0.0ms	(fma a c (* b d))
5.0ms	(/ (fma a c (* b d)) (fma c c (* d d)))

series186.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(fma a c (* b d))
133.0ms	(/ (fma a c (* b d)) (fma c c (* d d)))

simplify2.5s

Counts

45 → 45

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	64	725
1	101	714
2	249	622
3	725	622
4	2204	622
done	5001	622

prune196.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 16.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (hypot c d))
0.3b	(* (/ 1 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
0.8b	(fma a c (* b d))
15.7b	(/ (fma a c (* b d)) (hypot c d))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
43×	`times-frac`
36×	`*-un-lft-identity`
34×	`add-cube-cbrt`
32×	`add-exp-log`
20×	`add-cbrt-cube`
13×	`associate-r` `associate-l`
11×	`div-exp`
8×	`prod-exp`
7×	`pow1`
6×	`cbrt-undiv` `associate-/r` `associate-/l` `unswap-sqr`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`rec-exp` `1-exp`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `pow-flip` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `fma-udef` `inv-pow`

Counts

4 → 130

Calls

4 calls:

10.0ms	(/ 1 (hypot c d))
39.0ms	(* (/ 1 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
0.0ms	(fma a c (* b d))
6.0ms	(/ (fma a c (* b d)) (hypot c d))

series562.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(/ 1 (hypot c d))
264.0ms	(* (/ 1 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
62.0ms	(fma a c (* b d))
163.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify3.6s

Counts

142 → 142

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	153	2192
1	351	2009
2	1095	1759
3	3969	1759
done	5000	1726

prune492.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 6.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot c d)
0.1b	(/ (/ (fma a c (* b d)) (hypot c d)) (hypot c d))
0.8b	(fma a c (* b d))
15.7b	(/ (fma a c (* b d)) (hypot c d))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
54×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`associate-/l*`
11×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*` `div-inv`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`hypot-udef` `fma-udef` `associate-/l/`

Counts

4 → 121

Calls

4 calls:

0.0ms	(hypot c d)
11.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (hypot c d))
0.0ms	(fma a c (* b d))
5.0ms	(/ (fma a c (* b d)) (hypot c d))

series387.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(hypot c d)
136.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (hypot c d))
62.0ms	(fma a c (* b d))
138.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify1.9s

Counts

133 → 133

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	167	2544
1	333	2481
2	714	2298
3	2050	2244
done	5000	2182

prune493.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1 (/ (hypot c d) (fma a c (* b d)))) (hypot c d))
0.2b	(/ 1 (/ (hypot c d) (fma a c (* b d))))
0.8b	(fma a c (* b d))
15.8b	(/ (hypot c d) (fma a c (* b d)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

480×	`times-frac`
239×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
50×	`associate-/l*`
36×	`add-exp-log`
23×	`div-inv`
22×	`div-exp`
20×	`add-cbrt-cube`
19×	`associate-/r*`
10×	`cbrt-undiv`
5×	`pow1` `associate-/r/`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
1×	`pow-flip` `fma-udef` `associate-/l/` `inv-pow`

Counts

4 → 319

Calls

4 calls:

35.0ms	(/ (/ 1 (/ (hypot c d) (fma a c (* b d)))) (hypot c d))
10.0ms	(/ 1 (/ (hypot c d) (fma a c (* b d))))
0.0ms	(fma a c (* b d))
7.0ms	(/ (hypot c d) (fma a c (* b d)))

series591.0ms

Counts

4 → 12

Calls

4 calls:

235.0ms	(/ (/ 1 (/ (hypot c d) (fma a c (* b d)))) (hypot c d))
140.0ms	(/ 1 (/ (hypot c d) (fma a c (* b d))))
59.0ms	(fma a c (* b d))
157.0ms	(/ (hypot c d) (fma a c (* b d)))

simplify1.7s

Counts

331 → 331

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	458	8797
1	1013	7708
2	1901	7150
done	5000	6968

prune778.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 6.5b

regimes356.0ms

Accuracy

35.7% (7.0b remaining)

Error of 13.0b against oracle of 6.0b and baseline of 16.9b

bsearch129.0ms

Steps

Iters	Range		Point
9	5.148798436504621e+206	6.633447625029813e+211	1.0368644268796637e+207
10	-3.1661596442426373e+173	-4.4874797001979404e+160	-1.2861841180889815e+163

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	23	41
1	30	35
2	34	35
done	34	35

end0.0ms

sample1.3s

Algorithm

intervals

Results

906.0ms

8494×

body

valid